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Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…
Models issued from ecology, chemical reactions and several other application fields lead to semi-linear parabolic equations with super-linear growth. Even if, in general, blow-up can occur, these models share the property that mass control…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems. Response lags are required by most of physical systems and play a key role in the feedback…
This paper provides global exponential stabilization results by means of boundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial Differential Equations (PDEs) with nonlinearities of superlinear growth. The class of…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
We obtain classification, solvability and nonexistence theorems for positive stationary states of reaction-diffusion and Schr\"odinger systems involving a balance between repulsive and attractive terms. This class of systems contains PDE…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output…
We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…
We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the…
In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…
We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a…
This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency domain controllability criteria. Firstly, we derive a controllability…
In \cite{LPP:2025}, it was shown that, in arbitrary dimension, the spatial semi-discretization of a controlled stochastic parabolic operator is generically not null-controllable. Nevertheless, $\phi$-null controllability results remain…
We give the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space. Formally we give a…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
A reaction-diffusion equation is studied in a time-dependent interval whose length varies with time. The reaction term is either linear or of KPP type. On a fixed interval, it is well-known that if the length is less than a certain critical…